非平稳序列的确定性分析.docx
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非平稳序列的确定性分析
非平稳序列的确定性分析
1、首先画出时序图如下：
从时序图可以看出这显然是一个非平稳序列，而其又呈现出指数增长趋势，因此考虑拟合非线性模型：
利用sas计算得到拟合模型为：
拟合图如下：
检验：
SumofMeanApprox
SourceDFSquaresSquareFValuePr>FModel21.26E116.3E101778.88<.0001
Error258.8539E835415408
CorrectedTotal271.269E11
Approx
ParameterEstimateStdErrorApproximate95%ConfidenceLimits
a-3989.13179.5-10537.32559.1
b6365.51085.94129.08602.0
c0.13050.006060.11800.1430
可以看到各项检验都通过。
接下来对残差进行白噪声检验：
残差计算为：
检验：
AutocorrelationCheckforWhiteNoise
ToLagChiSquareDFPr>ChiSq--------------------Autocorrelations--------------------
657.366<.00010.7790.4370.009-0.370-0.574-0.637
1272.3112<.0001-0.474-0.264-0.0570.0900.1550.157
可以看出p值都小于0.05，没有通过检验，考虑到其指数趋势，因对序列取对数，得到时序图：
取对数后的序列呈现线性增长趋势，对取对数后的数据进行一阶差分，时序图：
再进行平稳性检验：
Autocorrelations
LagCovarianceCorrelation-198765432101234567891StdError
00.00394911.00000||********************|0
10.00241540.61164|.|************|0.192450
20.000700150.17730|.|****.|0.254457
3-0.0005546-.14045|.***|.|0.258992
4-0.0014108-.35726|.*******|.|0.261798
5-0.0015622-.39558|.********|.|0.279272
6-0.0011031-.27934|.******|.|
可以看出序列已经平稳。
所以接下来根据平稳序列建模预测：
根据之前平稳序列分析并利用sas可知模型为：
（平稳序列建模过程略）
预测图为：
本题代码：
dataaa;
inputgdp@@;
t=intnx（'year','01jan1980'd,_n_-1）;
formattyear4.;
cards;
4517.84862.45294.75934.571718964.410202.2
11962.514928.316909.218547.921617.826638.134634.4
46759.458478.167884.674462.678345.282067.589442.2
97314.8118020.7135822.8159878.3183217.4211923249530
;
procgplot;
plotgdp*t;symbolc=bluei=jionv=dot;
run;
databb;
inputx_t@@;
t=_n_;
cards;
4517.84862.45294.75934.571718964.410202.2
11962.514928.316909.218547.921617.826638.134634.4
46759.458478.167884.674462.678345.282067.589442.2
97314.8118020.7135822.8159878.3183217.4211923249530
;
procnlinmethod=gauss;modelx_t=a+b*exp（c*t）;
parametersa=1b=0.5c=0.5;
der.a=1;der.b=exp（c*t）;der.c=t*b*exp（c*t）;
outputpredicted=x_thatout=result;
run;
procgplotdata=result;plotx_t*t=1x_that*t=2/overlay;
symbol1c=blacki=nonev=dotl=1w=1;
symbol2c=bluei=jionv=dotl=2w=2;
run;
datacc;
inputx_t@@;t=_n_;
epli=x_t+3989.1-6365.5*exp（0.1305*t）;
cards;
4517.84862.45294.75934.571718964.410202.2
11962.514928.316909.218547.921617.826638.134634.4
46759.458478.167884.674462.678345.282067.589442.2
97314.8118020.7135822.8159878.3183217.4211923249530
;
procarima;identifyvar=eplinlag=12;
run;
datadd;
inputgdp@@;y=log（gdp）;
t=intnx（'year','01jan1980'd,_n_-1）;
formattyear4.;
cards;
4517.84862.45294.75934.571718964.410202.2
11962.514928.316909.218547.921617.826638.134634.4
46759.458478.167884.674462.678345.282067.589442.2
97314.8118020.7135822.8159878.3183217.4211923249530
;
procgplot;
ploty*t;symbolc=bluei=jionv=dot;
run;
dataee;
inputgdp@@;y=log（gdp）;y1=dif（y）;
t=intnx（'year','1jan1980'd,_n_-1）;
formattyear4.;
cards;
4517.84862.45294.75934.571718964.410202.2
11962.514928.316909.218547.921617.826638.134634.4
46759.458478.167884.674462.678345.282067.589442.2
97314.8118020.7135822.8159878.3183217.4211923249530
;
procgplot;
ploty1*t;symbolc=bluei=jionv=dot;
procarimadata=ee;
identifyvar=y
（1）nlag=8minicp=（0:
5）q=（0:
5）;
estimatep=1;
forecastlead=5id=tinterval=yearout=results;
procgplotdata=results;
ploty*t=1forecast*t=2l95*t=3u95*t=3/overlay;
symbol1c=blueki=jionv=star;
symbol2c=redi=jionv=nonel=1w=1;
symbol3c=greeni=jionv=nonel=2w=2;
run;
2、首先画出时序图：
从时序图中我们发现生猪屠宰量随季节变动较强，对序列进行平稳性检验：
Autocorrelations
LagCovarianceCorrelation-198765432101234567891StdError
01974413671.00000||********************|0
11080958560.54748|.|***********|0.062257
2942926080.47757|.|**********|0.078737
31013850020.51349|.|**********|0.089261
4722588600.36598|.|*******|0.100058
5849071260.43004|.|*********|0.105118
6754987130.38239|.|********|0.111729
7700354350.35472|.|*******|0.116691
8660856120.33471|.|*******|0.120798
9695059990.35203|.|*******|0.124341
10600090070.30393|.|******|0.128146
11712799720.36102|.|*******|0.130910
12925196690.46859|.|*********|
发现其相关系数并没有落在两倍标准差之内，这是个非平稳序列。
接下来使用x11过程进行季节调整得到平均季节指数图：
消除季节趋势后得到的序列图如下：
可以看出，剔除季节效应后序列呈现不规则的波动，并没有明显的递增或下降趋势。
使用移动平均方法拟合得到：
随机波动项：
从中可以看出x11过程对季节效应提取比较充分。
接下来预测未来一年的屠宰数据：
ParameterEstimates
VariableDFEstimateErrortValuePr>|t|
Intercept1102481135375.76<.0001
t1-102.335711.6710-8.77<.0001
对趋势项trend拟合的线性回归模型为：
以1994年9月到1995年8月季节指数作为1995年9月到1996年8月季节指数进行预测如下：
ObstSEASONtrendpx
1196099.46883139.5582697.63
21960107.12683037.2288954.68
3196089.67782934.8874373.21
4196095.66682832.5579242.33
51960107.44482730.2188888.74
6196090.89882627.8775107.18
7196099.45382525.5482074.44
8196097.19482423.2080110.21
91960105.64682320.8786968.96
101960104.30582218.5385757.87
11196099.50882116.2081712.47
121960103.30782013.8684726.13
本题代码：
dataa;
inputx@@;
t=intnx（'month','1jan1980'd,_n_-1）;
formattyear4.;
cards;
763787194733873964281050849574111064710033194133103055
905951014577688981291916439622810273610026410349197027
9524091680101259109564768928577395210937719820297906
100306940891026807791993561117062812258835710617591922
1041141099599788010538696479975801094901101919097498981
1071889417711509711369611453212011093607110925103312120184
103069103351111331106161111590994471019878533386970100561
763787194733873964281050849574111064710033194133103055
905951014577688981291916439622810273610026410349197027
9524091680101259109564768928577395210937719820297906
100306940891026807791993561117062812258835710617591922
1041141099599788010538696479975801094901101919097498981
1071889417711509711369611453212011093607110925103312120184
103069103351111331106161111590994471019878533386970100561
89543892658271979498748467381977029784468697875878
69571757226418277357632925938078332723815597169750
85472701337912585805817788685269069795568817466698
72258734457613186082754437396978139786466626973776
8003470694818237564075540822297534577034
;
procx11data=a;
monthlydate=t;varx;
outputout=outb1=xd10=seasond11=adjusted
d12=trendd13=irr;
datab;
setout;
t=_n_;
run;
procprintdata=b;
procautoregdata=b;
modeltrend=t;
run;
databb;
setout;
keeptseason;
if'01sep1994'd<=t<='01aug1995'dthenoutput;
run;
datac;
dot=189to200;
trend=102481-102.3357*t;
output;
end;
run;
datayuce;
mergebbc;
px=season*trend/100;
procprintdata=yuce;
run;
3、时序图如下：
从中可以发现该序列有明显的季节递增特征，因此尝试混合模型：
计算得到季节指数为：
Obsmonthindex
112.84293
222.72986
332.66264
442.63650
552.67869
662.75406
772.68929
882.71988
992.92208
10103.05008
11113.18537
12123.86366
季节指数图：
生成消除季节影响后趋势序列：
因为序列的时序图显示该序列有一个基本线性递增的趋势，故用一元线性回归模型对其进行拟合。
对趋势序列拟合线性回归模型：
ParameterEstimates
ParameterStandard
VariableDFEstimateErrortValuePr>|t|
Intercept11015.5222026.8266337.86<.0001
t120.931780.4802643.58<.0001
该线性趋势模型为：
接下来生成随机波动序列进行向前一年预测：
Obsindexptpxtime
10.982153045.932991.572001
20.943093066.862892.332001
30.919873087.792840.362001
40.910843108.722831.542001
50.925413129.652896.222001
60.951453150.592997.632001
70.929083171.522946.582001
80.939653192.452999.772001
91.009503213.383243.902001
101.053723234.313408.062001
111.100463255.253582.262001
121.334793276.184373.012001
最后绘制序列实际值和预测值的拟合图如下：
本题代码：
databin1;
doyear=1993to2000;
domonth=1to12;
inputmilk@@;
output;
end;
end;
cards;
977.5892.5942.3941.3962.21005.7963.8959.81023.31051.111021415.5
1192.21162.71167.51170.41213.71281.11251.512861396.21444.11553.81932.2
1602.21491.51533.31548.71585.41639.71623.61637.1175618181935.22389.5
1909.11911.21860.11854.81898.319661888.71916.42083.52148.32290.12848.6
2288.52213.52130.92100.52108.22164.72102.52104.42239.623482454.92881.7
2549.52306.42279.72252.72265.223262286.12314.62443.125362652.23131.4
2662.12538.42403.12356.823642428.82380.32410.92604.32743.92781.53405.7
2774.728052627257226372645259726362854302931083680
;
databin1;
setbin1;
time=intnx（'month','1jan1993'd,_n_-1）;
formattimeyear4.;
procprint;
procgplotdata=bin1;
plotmilk*time/haxis='1jan1993'dto'1jan2000'dbyyear;
symbolc=bluei=joinv=none;
run;
procsql;
selectavg（milk）
frombin1;
run;
procsql;
createtablebin2（monthnum,indexnum）;
insertintobin2
selectmonth,avg（milk）/2030.7135asindex
frombin1
groupbymonth;
quit;
run;
procprintdata=bin2;
run;
procgplotdata=bin2;
plotindex*month/vaxis=0.9to1.35by0.05;
symbolc=bluei=joinv=square;
run;
procsortdata=bin1out=bin3;
bymonthyear;
databin4;
mergebin2bin3;
bymonth;admilk=milk/index;
procprint;run;
procsortdata=bin4out=bin5;
byyearmonth;
procgplotdata=bin5;
plotadmilk*time/haxis='1jan1993'dto'1jan2000'dbyyear;
symbolc=bluei=nonev=circle;
run;
databin5;
setbin5;
t=_n_;
procreg;
modeladmilk=t;
outputp=pmilkout=trend;
procgplot;
plotpmilk*t=1admilk*t=2/overlay;
symbol1i=joinc=greenv=none;
symbol2i=nonec=bluev=circle;
run;
databin6;
settrend;
noise=admilk-pmilk;
keepnoisem;
procgplotdata=bin6;
plotnoise*m;
symboli=nonec=bluev=circl
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